ABSTRACT
Those unfamiliar with the concepts involved in Fourier analysis and wavelets may have found some statements in the main article a bit mysterious. We said that the Fourier transform breaks down a signal by frequency, and that the wavelet transform breaks down a signal into components of different scales by comparing the signal to wavelets of different sizes. In both cases, we said, this is done by integration: multiplying the signal by the analyzing function (sines and cosines or wavelets) and integrating the product. Why does calculating integrals allow us to decompose a signal? If you glance at any signal-processing or wavelet text, you'll see that mathematicians and engineers refer to computing Fourier or wavelet coefficients as taking the scalar product of the signal and the analyzing function. (Sometimes, to add to the confusion, they call it a dot product or inner product.) If the technique used is integration, why drag in dot, scalar, or inner products?
